21 Problems For The Twenty-First Century

The dawning of the twenty-first century provides a rare opportunity for looking ahead, a time of speculating, and a chance for identifying specific challenges of a mathematical kind. Only recently, a worldwide survey of mathematicians focused on this special event and thus provided a brief assessment of the century past, an inventory in reference to the present, and a consideration of trends foreshadowing the mathematical course of action in the decades before us. The sentiment of the response was essentially one of a golden era now drawing to a close even as another golden time period awaits.

Table of Contents:

THE PAST, THE PRESENT

TWENTY-ONE PROBLEMS: A CHALLENGE
The Mersenne Prime Problem
The Constructibility Problem
The Prime Generation Problem
The Digital Frequency Problem
The Problem of Transcendence
The Dirichlet Generalization Problem
Waring's Problem Extended
Classification of Euler's Constant
Cardinality of the Set of Repunit Primes
The Two Prime Representation Problem
The Twin Prime Problem
The Lemma Dilemma
The Odd Perfect Number Problem
Catalan's Problem
The Square-Betweenness Problem
The Pythagorean Prime Problem
Euclidean Prime Problem
The Zero-One Problem
The Factorially Based Prime Problem
Absolute Unit of Measure Problem
The Power Expression Problem

PREDICTIONS

REFERENCES